Illustrating Dynamical Symmetries in Classical Mechanics: The Laplace-Runge-Lenz Vector Revisited

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and degeneracy associated with this vector and with analogous dynamical symmetris. We define a conserved dynamical variable $\alpha$ that characterizes the orientation of the orbit in two-dimensional configuration space for the Kepler problem and an analogous variable $\beta$ for the isotropic harmonics oscillator. This orbit orientation variable is canonically conjugate to the angular momentum component normal to the plane of motion. We explore the canoncial one-parameter group of transformations generated by $\alpha (\beta).$ Because we have an obvious pair of conserved canonically conjugate variables, it is desirable to us them as a coordinate-momentum pair. In terms of these phase space coordinates, the form of the Hamiltonian is nearly trivial because neither member of the pair can occur explicitly in the Hamiltonian. From these considerations we gain a simple picture of the dynamics in phase space. The procedure we use is in the spirit of the Hamilton-Jacobi method.Comment: 15 pages, 1 figure, to be published in American Journal of Physic

RascalC: A Jackknife Approach to Estimating Single and Multi-Tracer Galaxy Covariance Matrices

To make use of clustering statistics from large cosmological surveys, accurate and precise covariance matrices are needed. We present a new code to estimate large scale galaxy two-point correlation function (2PCF) covariances in arbitrary survey geometries that, due to new sampling techniques, runs $\sim 10^4$ times faster than previous codes, computing finely-binned covariance matrices with negligible noise in less than 100 CPU-hours. As in previous works, non-Gaussianity is approximated via a small rescaling of shot-noise in the theoretical model, calibrated by comparing jackknife survey covariances to an associated jackknife model. The flexible code, RascalC, has been publicly released, and automatically takes care of all necessary pre- and post-processing, requiring only a single input dataset (without a prior 2PCF model). Deviations between large scale model covariances from a mock survey and those from a large suite of mocks are found to be be indistinguishable from noise. In addition, the choice of input mock are shown to be irrelevant for desired noise levels below $\sim 10^5$ mocks. Coupled with its generalization to multi-tracer data-sets, this shows the algorithm to be an excellent tool for analysis, reducing the need for large numbers of mock simulations to be computed.Comment: 29 pages, 8 figures. Accepted by MNRAS. Code is available at http://github.com/oliverphilcox/RascalC with documentation at http://rascalc.readthedocs.io

Temporal and spatial trends in stranding records of cetaceans on the Irish coast, 2002–2014

Using Irish strandings data collected between 2002 and 2014, seasonal and annual trends in the number of strandings for all strandings identified to species level (N ¼ 1480), and for the five most frequently reported species: common dolphin (25.7% of records), harbour porpoise (22.2%), long-finned pilot whale (8.8%), striped dolphin (6.9%) and bottlenose dolphin (6.9%) were investigated. With the exception of bottlenose dolphins, there was a significant linear increase in the number of strandings across years for all species and for all strandings collectively, that were identified to species-level. Only common dolphins demonstrated a significant increase in the proportion of records relative to all other strandings, which may be indicative of a real rise in the number of strandings of this species. Common dolphins and harbour porpoises showed a similar significant difference in monthly strandings, with more strandings occurring during the earlier months of the year.\ud Significant differences in the gender of stranded animals were found in common, striped, bottlenose and Atlantic white-sided dolphins and sperm and pygmy sperm whales. Live and mass stranding events were primarily comprised of pelagic species. Most strandings occurred on the south and west coasts, with two hotspots for live and mass strandings identified. The patterns and trends identified are discussed in relation to the caveats in interpreting strandings data. Specifically to Ireland, the findings highlight the urgent need to build on the current volunteer reporting network and augment this comprehensive dataset with post-mortem examinations to better understand the cause of the trends identified. The importance of strandings data in informing conservation and management guidelines of these species’ is discussed

In Silico Assigned Resistance Genes Confer Bifidobacterium with Partial Resistance to Aminoglycosides but Not to Β-Lactams

peer-reviewedBifidobacteria have received significant attention due to their contribution to human gut health and the use of specific strains as probiotics. It is thus not surprising that there has also been significant interest with respect to their antibiotic resistance profile. Numerous culture-based studies have demonstrated that bifidobacteria are resistant to the majority of aminoglycosides, but are sensitive to β-lactams. However, limited research exists with respect to the genetic basis for the resistance of bifidobacteria to aminoglycosides. Here we performed an in-depth in silico analysis of putative Bifidobacterium-encoded aminoglycoside resistance proteins and β-lactamases and assess the contribution of these proteins to antibiotic resistance. The in silico-based screen detected putative aminoglycoside and β-lactam resistance proteins across the Bifidobacterium genus. Laboratory-based investigations of a number of representative bifidobacteria strains confirmed that despite containing putative β-lactamases, these strains were sensitive to β-lactams. In contrast, all strains were resistant to the aminoglycosides tested. To assess the contribution of genes encoding putative aminoglycoside resistance proteins in Bifidobacterium sp. two genes, namely Bbr_0651 and Bbr_1586, were targeted for insertional inactivation in B. breve UCC2003. As compared to the wild-type, the UCC2003 insertion mutant strains exhibited decreased resistance to gentamycin, kanamycin and streptomycin. This study highlights the associated risks of relying on the in silico assignment of gene function. Although several putative β-lactam resistance proteins are located in bifidobacteria, their presence does not coincide with resistance to these antibiotics. In contrast however, this approach has resulted in the identification of two loci that contribute to the aminoglycoside resistance of B. breve UCC2003 and, potentially, many other bifidobacteria.Fiona Fouhy is in receipt of an Irish Research Council for Science, Engineering and Technology EMBARK scholarship and is a Teagasc Walsh fellow. Research in the PDC laboratory is supported by the Irish Government under the National Development Plan through the Science Foundation Ireland Investigator award 11/PI/1137. Research in the RPR, CS, PDC and DvS laboratories is also supported by the Science Foundation of Ireland-funded Centre for Science, Engineering and Technology, the Alimentary Pharmabiotic Centre (grant no.s 02/CE/B124 and 07/CE/B1368) and a HRB postdoctoral fellowship (Grant no. PDTM/20011/9) awarded to MOCM

SDSS-III Baryon Oscillation Spectroscopic Survey: Analysis of Potential Systematics in Fitting of Baryon Acoustic Feature

Extraction of the Baryon Acoustic Oscillations (BAO) to percent level accuracy is challenging and demands an understanding of many potential systematic to an accuracy well below 1 per cent, in order ensure that they do not combine significantly when compared to statistical error of the BAO measurement. Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) SDSS Data Release Eleven (DR11) reaches a distance measurement with $\sim 1\%$ statistical error and this prompts an extensive search for all possible sub-percent level systematic errors which could be safely ignored previously. In this paper, we analyze the potential systematics in BAO fitting methodology using mocks and data from BOSS DR10 and DR11. We demonstrate the robustness of the fiducial multipole fitting methodology to be at $0.1\%-0.2\%$ level with a wide range of tests in mock galaxy catalogs pre- and post-reconstruction. We also find the DR10 and DR11 data from BOSS to be robust against changes in methodology at similar level. This systematic error budget is incorporated into the the error budget of Baryon Oscillation Spectroscopic Survey (BOSS) DR10 and DR11 BAO measurements. Of the wide range of changes we have investigated, we find that when fitting pre-reconstructed data or mocks, the following changes have the largest effect on the best fit values of distance measurements both parallel and perpendicular to the line of sight: (a) Changes in non-linear correlation function template; (b) Changes in fitting range of the correlation function; (c) Changes to the non-linear damping model parameters. The priors applied do not matter in the estimates of the fitted errors as long as we restrict ourselves to physically meaningful fitting regions.[abridged

Sloan Digital Sky Survey III Photometric Quasar Clustering: Probing the Initial Conditions of the Universe using the Largest Volume

The Sloan Digital Sky Survey has surveyed 14,555 square degrees of the sky, and delivered over a trillion pixels of imaging data. We present the large-scale clustering of 1.6 million quasars between z = 0.5 and z = 2.5 that have been classified from this imaging, representing the highest density of quasars ever studied for clustering measurements. This data set spans ~11,000 square degrees and probes a volume of 80(Gpc/h)^3. In principle, such a large volume and medium density of tracers should facilitate high-precision cosmological constraints. We measure the angular clustering of photometrically classified quasars using an optimal quadratic estimator in four redshift slices with an accuracy of ~25% over a bin width of l ~10 - 15 on scales corresponding to matter-radiation equality and larger (l ~ 2 - 30). Observational systematics can strongly bias clustering measurements on large scales, which can mimic cosmologically relevant signals such as deviations from Gaussianity in the spectrum of primordial perturbations. We account for systematics by employing a new method recently proposed by Agarwal et al. (2014) to the clustering of photometrically classified quasars. We carefully apply our methodology to mitigate known observational systematics and further remove angular bins that are contaminated by unknown systematics. Combining quasar data with the photometric luminous red galaxy (LRG) sample of Ross et al. (2011) and Ho et al. (2012), and marginalizing over all bias and shot noise-like parameters, we obtain a constraint on local primordial non-Gaussianity of fNL = -113+/-154 (1\sigma error). [Abridged]Comment: 35 pages, 15 figure